The labels, including divisions of Sony, Warner and Universal, argue that songs such as Aretha Franklin's "Respect" and the Beatles' "Hey Jude" are not covered by federal copyright law, but they have been protected in common law by states including New York.
In the lawsuit filed in New York state court, the labels say artists and labels have been deprived of tens of millions of dollars every year by services such as Pandora Media Inc.
Pandora streams songs randomly according to artists or genres like "Motown" or "'60s Oldies."
The labels also sued satellite radio company Sirius XM Holdings Inc. last year in a similar case.
Oakland, Calif.-based Pandora said in a statement that it "is confident in its legal position and looks forward to a quick resolution of this matter."